People often act on reciprocal habits, almost automatically respondingto others' actions. A robot who interacts with humans may also reciprocate, in order tocome across natural and to be predictable. We aim to facilitate a decision support system thatadvises on utility-efficient habits in these ubiquitous interactions.To this end, given a model for reciprocation behaviorwith parameters that represent habits,we define a game that describes which habit one should adoptto increase the utility of the process. The used modelspecifies an agent'saction as a weighted combination of the others' previous actions (reacting) and eitheri) her innate kindness, or ii) her own previous action (inertia).We analyze reciprocation attitude change only for a pairwise interaction,and the coefficient change for any number of agents.For the case of two agents,to analyze what happens when everyone reciprocates rationally,we define a game where an agent may choose her habit, which is either herreciprocation attitude (i or ii), orboth her reciprocation attitude and weight.For a general connected network, when all agents have attitude ii),we define a game where an agent chooses her weights.We characterize the Nash equilibria of these games and consider their efficiency.We find that the less kind agents should adjust to the kinder agentsto improve both their own utility as well as the social welfare.This constitutes advice on improving cooperation and explainsreal life phenomena in human interaction, suchas the societal benefits from adopting the behavior of the kindest person, orbecoming more polite as one grows up.

Abstract (2):

Consider people dividingtheir time and effort between friends, interest clubs, and reading seminars.These are all reciprocal interactions,and the reciprocal processes determine the utilitiesof the agents from these interactions. To advise on efficient effort division,we determine the existence and efficiency of the Nash equilibria of the game ofallocating effort to such projects. When no minimum effortis required to receive reciprocation, an equilibrium always exists, and ifacting is either easy to everyone, or hard to everyone, then every equilibriumis socially optimal. If a minimal effort is needed to participate,we prove that not contributing at all is an equilibrium, and for twoagents, also a socially optimal equilibrium can be found.Next, we extend the model, assuming that the need to reactrequires more than the agents can contribute to acting, renderingthe reciprocation imperfect.We prove that even then, each interaction convergesand the corresponding game has an equilibrium.